HDU 5229 ZCC loves strings

Problem Description

ZCC has got N strings. He is now playing a game with Miss G.. ZCC will pick up two strings among those N strings randomly(A string can't be chosen twice). Each string has the same probability to be chosen. Then ZCC and Miss G. play in turns. Miss G. always plays first. In each turn, the player can choose operation A or B.

Operation A: choose a non-empty string between two strings, and delete a single letter at the end of the string.

Operation B: When two strings are the same and not empty, empty both two strings.

The player who can't choose a valid operation loses the game.

ZCC wants to know what the probability of losing the game(i.e. Miss G. wins the game) is.

Input

T(T≤5) which denotes the number of test cases.

For each test case, there is an integer 

N(2≤N≤20000)

Output

For each test case, output an irreducible fraction "p/q" which is the answer. If the answer equals to 1, output "1/1" while output "0/1" when the answer is 0.

Sample Input

1

3

xllendone

xllendthree

xllendfour

Sample Output

2/3

#include<iostream>
#include<cmath>
#include<map>
#include<vector>
#include<queue>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int maxn = 100005;
int T, n, m, ans, a, b, A, B, C;
char s[maxn + maxn];

class tire
{
public:
    tire *next[26];
    int cnt;
    tire(){ cnt = 0; memset(next, 0, sizeof(next)); }
}*root;


int gcd(int x, int y)
{
    if (x%y) return gcd(y, x%y);
    return y;
}

void insert()
{
    tire *j = root;
    for (int i = 0; s[i]; i++)
    {
        if (!j->next[s[i] - 'a'])
        {
            j->next[s[i] - 'a'] = new tire;
        }
        j = j->next[s[i] - 'a'];
    }
    j->cnt++;
}

int dfs(tire *x)
{
    int tot = (x->cnt)*(x->cnt - 1) / 2;
    for (int i = 0; i < 26; i++)
        if (x->next[i]) tot += dfs(x->next[i]);
    return tot;
}

int main()
{
    scanf("%d", &T);
    while (T--)
    {
        scanf("%d", &n);
        a = b = A = B = 0;
        root = new tire;
        while (n--)
        {
            scanf("%s", s);
            insert();
            if (strlen(s) & 1) a++; else b++;
        }
        B = A = a * b;
        A += dfs(root);
        if (a > 1) B += a*(a - 1) / 2;
        if (b > 1) B += b*(b - 1) / 2;
        if (A) C = gcd(A, B);
        if (!A) printf("0/1\n");
        else printf("%d/%d\n", A / C, B / C);
    }
}